Uncovering emergent interactions in three-way combinations of stressors

Abstract

Understanding how multiple stressors interact is needed to predict the dynamical outcomes of diverse biological systems, ranging from drug-resistant pathogens that are combated and treated with combination drug therapies to ecosystems impacted by environmental toxicants or disturbances. Nevertheless, extensive studies of higher-order (more than two component) interactions have been lacking. Here, we conduct experiments using 20 threedrug combinations and their effects on the bacterial growth of Escherichia coli. We report our measurements of growth rates in single, pairwise and tripledrug combinations. To uncover emergent interactions, we derive a simple framework to calculate expectations for three-way interactions based on the measured impact of each individual stressor and of each pairwise interaction. Using our framework, we find that (i) emergent antagonisms are more common than emergent synergies and (ii) emergent antagonisms are more common and emergent synergies are more rare than would be inferred from measures of net effects that do not disentangle pairwise interactions from three-way interactions.

Enhanced identification of synergistic and antagonistic emergent interactions among three or more drugs

“…Overcoming this challenge often requires a rescaling or normalization of basic metrics, and for pairwise interactions, some effective methods have been discovered [8,[18][19][20]. Rescaling for combinations of more than two drugs has previously been done using the most straightforward generalization of the pairwise method [14,21], but unlike the pairwise case, there are several possibilities for rescaling metrics for higher order interactions, even among three drugs. Here, we explore these possible rescalings and identify the one that is best at categorizing and thus distinguishing among three-drug interactions.…”

“…Thus, a useful categorization scheme for interactions is needed that uses the additive case [6,12,13]-drugs do not interact at all-as a baseline. Along with this is the concept of emergence-effects of drug combinations that cannot be predicted from lower order interactions among subsets of the drugs [14]. Relative to these baselines, interactions are generally categorized as a type of synergy if the combination kills more efficiently than is expected from the additive case or from lower order interactions (figure 1).…”

“…Importantly, this particular rescaling method is different from the rescaling previously used in the literature by ourselves and others. Consequently, this could reveal new insights for interactions among three or more drugs, as well as other objects such as proteins [22] and predators [23][24][25][26][27], and some existing results may need to be revisited and revised [14,28].…”

“…Recently, a novel method to characterize and quantify emergent interactions in three-drug combinations has been introduced. Beppler et al [14] present a framework that compares the higher order interaction with expectations based on its lower order component interactions. First, the direct extension of the DA metric allows identification of three-drug interaction compared solely to the single-drug effects [14,21,29].…”

“…Beppler et al [14] present a framework that compares the higher order interaction with expectations based on its lower order component interactions. First, the direct extension of the DA metric allows identification of three-drug interaction compared solely to the single-drug effects [14,21,29]. Next, the new emergent three-way interaction (E3) incorporates the pairwise interactions in the model and determines the effect of three-drug interaction that is beyond the effects from all two-drug combinations.…”